AP® Chemistry - Thermodynamics

A thermodynamic system is a macroscopic body which is engaged in mass and/or energy exchange with its surroundings.

Ex: The classic example of a thermodynamic system is a piston filled with gas.

An open thermodynamic system can exchange both mass and energy with the environment.

Ex: A bottle of gas with no lid is an open thermodynamic system.

A closed thermodynamic system cannot exchange mass with the environment, but can exchange energy.

Ex: A bottle of gas with the lid securely on is a closed thermodynamic system.

An isolated thermodynamic system can not exchange either energy or mass with the environment.

Ex: A closed, double-walled (insulated) container which is temperature-independent of its environment is an isolated system.

The surroundings (also known as the environment) are everything capable of exchanging mass and/or energy with the system.

A state function is any property of a thermodynamic system that depends only on comparing the characteristics of the system at that moment compared to a prior moment.

Since state functions are calculated based on current vs past properties only, their values do not depend on the path by which the current state was achieved; they are path-independent.

ΔX = X2 - X1

Since X is a state function, the path by which it gets from state 1 to 2 is irrelevant, the change in X depends only on the starting and finishing states.

Enthalpy is a measure of the heat contained in a system.

Enthalpy’s absolute value cannot be directly measured, so the change in enthalpy’s value, ΔH, is measured instead.

An exothermic reaction is any reaction whose products have a lower enthalpy than the reactants. Therefore, ΔH < 0, and heat is lost from the system to the environment.

(Exo = exit)

An endothermic reaction is any reaction whose products have a higher enthalpy than the reactants. Therefore, ΔH > 0, and heat is absorbed by the system from the environment.

(Endo = into)

The standard enthalpy of formation (ΔHof) is the enthalpy change of the formation reaction for the material from its fundamental elements under standard conditions.

Ex: The enthalpy of formation for NaCl is -411.12 kJ mol−1 and follows from the general equation:

Zero.

By definition, the enthalpy of formation for any material in its standard state is zero.

Standard conditions for a reaction require that:

Pressure = 1 atm

Temperature = 25º C = 298 K

Concentration = 1 M for all products and reactants

ΔH1 = ΔH2 + ΔH3

Hess’s Law simply states that the enthalpy of a reaction can be calculated by adding together the enthalpies of a chain of sub-reactions which add up to the overall reaction.

Although most commonly applied to enthalpy, Hess’s Law applies to all state functions.

-152 kJ

Adding the reactions together yields the formation reaction of CH4:

C(s) + 4H(g) + 2H2(g) ⇒

CH4(g) + 4H(g)

Canceling common terms leaves:

C(s) + 2H2(g) ⇒CH4(g)

To complete the calculation, combine the reactions’ enthalpies in the same way the reactions were combined.

ΔHrxn = ΔH1 + ΔH2

-870 + 794 = -76kJ/mol

Finally, multiply by the number of moles (2) to get the final answer.

∆Hºrxn= Σ∆Hºf(products)-Σ∆Hºf(reactants)

Sum the enthalpies of formation of the products, and subtract the sum of the enthalpies of formation of the reactants.

The reaction is exothermic.

∆H°rxn= Σ∆Hof(products)-Σ∆Hof(reactants)

= [CO2 + 2*H2O] - [CH4 + O2]

= [-394 kJ/mol + 2(-286 kJ/mol)]

- [-75 kJ/mol + 2(0 kJ)]

= -891 kJ/mol

Bond enthalpy is the energy absorbed or released when a particular chemical bond is broken.

Most chemical bonds are stabilizing, so most bond-breaking reactions are endothermic, and most bond enthalpies are positive.

∆Hrxn = Σ∆H(bonds broken) - Σ∆H(bonds formed)

The reaction’s enthalpy change is identical to the energy needed to break all the bonds in the reactants, minus the energy released when the bonds in the products form.

-818 kJ/mol

∆Hrxn = Σ∆H(bonds broken) - Σ∆H(bonds formed)

= [4*(C-H) + 2*(O=O)] - [2*(C=O) + 2*2*(H-O)]

= [(4 411) + (2 494)]

- [(2 799) + (4 463)] kJ/mol

= -818 kJ/mol

Specific heat is a characteristic property of a material, and is the amount of heat which must be added to raise 1 g of the substance by 1ºC.

The higher the value of c, the more heat it takes to raise the substance’s temperature.

q = mcΔT

Where q is the necessary heat, m is the mass of substance present, c is the substance’s specific heat, and ΔT is the desired temperature change.

4.184 J/g*K

This is a value that you should have memorized. It means that it takes 4.184 J to raise 1 g of water by 1ºK.

This value is equal to 1 cal/g*K.

The iron changes its temperature more.

Applying the equation q = mcΔT to both cases and solving for ΔT reveals that the iron will change temperature by about 20 degrees (final T = 45ºC), while the water will only increase by 2 degrees (final T = 27ºC).

The higher a material’s specific heat, the less responsive its temperature is to heat flow.

A calorimeter measures the amount of heat given off by a particular chemical reaction or process.

There are many different styles of calorimeter, but for most chemistry courses, including the AP Chemistry exam, you should focus on the fact that they all measure heat generated via a system's temperature change, using the equation

q = mcΔT

During a phase change, temperature stays constant as heat is added. The added heat causes the material to go through the phase change, rather than increasing its temperature.

The amount of heat needed to make a material change its phase is known as the latent heat of that phase change.

q = mΔHL

where q = necessary heat, m = mass of the substance present, and ΔHL is the latent heat of the phase change.

The higher the ΔHL, the more heat it takes to force the substance to go through the phase change.

a. solid

b. both solid and liquid

c. liquid

d. both liquid and gas

e. gas

a. q=mcΔT

b. q=mΔHfus

c. q=mcΔT

d. q=mΔHvap

e. q=mcΔT

Entropy is a macroscopic property of a system, representing the number of possible ways the atoms or molecules of the system can arrange themselves.

Note: Colloquially, entropy is said to represent the 'possibility for disorder' of a system, and this definition is effective enough for most entropy questions on the AP Chem exam.

As a system's entropy increases, it becomes more disordered.

Systems spontaneously tend towards arrangements with higher entropy.

Ssolid \< Sliquid \< Sgas

Since entropy is a measure of disorder, the more ordered a system, the lower its entropy. Solid matter, with its regularly-repeating units and fairly well-defined locations for the atoms, is therefore low in entropy, while gases, with their continuous, random motion, have the highest entropy values.

ΔS \< 0

Gases have more entropy than liquids; hence, in any chemical reaction, the side with more moles of gas will have higher entropy.

In general, reactions with fewer moles of products than reactants will have lower final entropy.

ΔHrxn > 0

ΔSrxn > 0

The reaction is endothermic, since heat must be added to vaporize the water.

Since the reaction creates gas, it represents an increase in entropy.

ΔHrxn \< 0

ΔSrxn \< 0

The reaction is exothermic, since heat must be removed to deposit the CO2.

Since the reaction results in a net decrease of gas, it represents an decrease in entropy.

ΔG is a measure of the work which can be extracted from a thermodynamic system.

ΔG = ΔH - TΔS

It also is used to measure the spontaneity of a system; chemical systems will always tend to move in a direction of decreasing ΔG.

A handy mnemonic for remembering the formula for ΔG is: 'Get Higher Test Scores'.

If ΔG \< 0 for a chemical reaction, then the forward reaction is spontaneous, favoring the creation of more products.

If ΔG > 0 for a chemical reaction, then the forward reaction is non-spontaneous, and the reverse reaction is spontaneous, favoring the creation of more reactants.

An exergonic reaction is any reaction for which ΔG \< 0; hence all exergonic reactions are spontaneous.

This is very similar to the definition of exothermic, for which ΔH \< 0. "Thermic" refers to Enthalpy, "gonic" to Gibbs' Free Energy.

(Exerg = exit G)

An endergonic reaction is any reaction for which ΔG > 0; hence all endergonic reactions are non-spontaneous.

This is very similar to the definition of endothermic, for which ΔH > 0. "Thermic" refers to Enthalpy, "gonic" to Gibbs' Free Energy.

(Enderg = enter G)

This reaction will always be non-spontaneous.

Remember, ΔG = ΔH - TΔS. Since T is in Kelvin and will always be positive, then both ΔH and -TΔS are positive. The quantity ΔG will always be positive then, so the reaction is endergonic at all temperatures.

This reaction will be spontaneous at low temperatures, and non-spontaneous at sufficiently high temperatures.

Remember, ΔG = ΔH - TΔS. When T is low (near zero Kelvin), the second term can be ignored, and ΔG will be negative due to ΔH\<0. But when T becomes large enough, the positive sign of the -TΔS term dominates, and ΔG becomes positive.

This reaction will be spontaneous at high temperatures and non-spontaneous at sufficiently low temperatures.

Remember, ΔG = ΔH - TΔS. When T is low (near zero Kelvin), the second term can be ignored, and ΔG will be positive due to ΔH>0. But when T becomes large enough, the negative sign of the -TΔS term dominates, and ΔG becomes negative.

This reaction will always be spontaneous.

Remember, ΔG = ΔH - TΔS. Since T is in Kelvin and will always be positive, both ΔH and -TΔS are negative. The quantity ΔG will always be negative, so the reaction is exergonic at all temperatures.

ΔG describes the change in Gibbs' Free Energy for a chemical system at a particular pressure and temperature, which must be given.

ΔGº describes the change in Gibbs' Free Energy for a chemical system at standard conditions (1 atm, 298 K, 1 M in all concentrations).

Typically, different reactions' ΔGº values will be compared, since this gives a common point of reference between them.

Temperature and internal energy are equivalent concepts.

Ex: If a system's absolute temperature doubles, so does the amount of energy that it contains.

This is the foundation of the zeroth law of thermodynamics, which states that if systems A and C are both in thermal equilibrium with system B, they are also in equilibrium with each other; i.e. they are at the same temperature.

U = KEavg = (3/2)nkT

k is Boltzmann's constant(1.38x10-23 J/K);

T is the absolute temperature (in Kelvin);

n is the number of moles of fluid molecules (in mol)

Work is the flow of energy between a system and its surroundings in the form of changing pressure and volume of the system.

In thermodynamics, work is signified by the symbol w.

Heat is the flow of energy between a system and its surroundings in any form other than work.

In thermodynamics, heat is signified by the symbol q.

The First Law of Thermodynamics states that heat and work are the only ways in which energy can flow, and energy is always conserved, hence energy change can be calculated:

ΔE = Δq + Δw

During a compression, work is being done by the environment, and on the system.

Since energy is flowing into the system due to the work being done, ΔE > 0.

During an expansion, work is being done by the system, and on the environment.

Since energy is flowing out of the system due to the work being done, ΔE \< 0.

When the environment is at a higher temperature than the system, heat flows from the environment into the system, and Δq > 0.

This direction of heat flow leads to energy being added to the system, and ΔE > 0.

When the environment is at a lower temperature than the system, heat flows from the system to the environment, and Δq \< 0.

This direction of heat flow leads to energy being removed from the system, and ΔE \< 0.

An adiabatic process is any process where heat cannot flow. Hence, Δq = 0 and ΔE = Δw; all energy change is due to work being done on or by the system.

Adiabatic processes are processes that happen in either heat-insulated systems, or that happen so quickly that heat cannot flow between system and environment.

The system's temperature must increase during an adiabatic compression.

Remember, Δq = 0 for all adiabatic processes. Furthermore, during any compression, work is being done on the system, raising ΔE. Since T and ΔE are proportional, the system must gain temperature during an adiabatic compression.

The system's temperature must decrease during an adiabatic expansion.

Remember, Δq = 0 for all adiabatic processes. Furthermore, during any expansion, the system is doing work, causing it to lose energy. Since T and ΔE are proportional, the system must lose temperature during an adiabatic expansion.

An isothermal process is any process where temperature is held constant. Hence, ΔE = 0, and Δq = -Δw. Any heat flow into or out of the system is compensated by work done by or on the system, respectively.

Isothermal processes are usually processes that happen slowly enough that the system's temperature can constantly equilibrate.

Heat flows out of the system during an isothermal compression.

Remember, during any compression, work is being done on the system, raising ΔE. Since an isothermal compression must have an overall ΔE = 0, Δq must be negative to compensate.

Heat flows into the system during an isothermal expansion.

Remember, during any expansion, the system is doing work, losing energy. Since any isothermal process must have an overall ΔE = 0, Δq must be positive to compensate.

The Second Law of Thermodynamics states that for any thermodynamic process, the total entropy of the universe increases.

ΔSuniverse > 0

ΔSsystem+ ΔSsurroundings > 0

since the universe can be defined as a system and its surroundings. If the entropy of a system decreases, therefore, the entropy of its surroundings must increase by a greater amount in order for the universal law to still hold true.

ΔSX > 0

Since System X is isolated it cannot exchange energy or entropy with its surroundings. For the Second Law to hold, the system's entropy must increase.

TK = TC + 273

TK = Kelvin Temperature

TC = Celsius Temperature

Some standard temperatures to memorize:

0º C = 273º K

25º C = 298º K

100º C = 373º K

TF = (9/5)*TC + 32

TF = Fahrenheit Temperature

TC = Celsius Temperature

Some standard conversions to memorize:

32º F = 0º C

77º F = 25º C

212º F = 100º C

Conduction is the transfer of thermal energy via molecular collisions. It requires physical contact between the systems exchanging energy.

When the molecules collide, molecules of the higher-energy system transfer some of their energy to the lower energy molecules of the other system, cooling the first and heating the second.

Convection is the thermal energy transfer via the movement of fluid in currents. It requires at least one medium which is capable of motion.

Differences in pressure or density drive warm fluid in the direction of cooler fluid, transferring heat away from a warmer object or towards a cooler one.

Radiation is the thermal energy transfer via emission or absorption of electromagnetic waves.

Radiation does not require a medium and can occur through a vacuum.

Conduction

Conduction is the most efficient form of heat transfer; since the metal and table are in direct physical contact, conduction transfer will dominate.

Convection

The decreased density of the warmer air causes it to rise to the top of the house, a classic example of a convection current.

Radiation

For the heat to get from the sun to the earth, it must travel across millions of miles of nearly empty space. Only electromagnetic radiation can carry energy across this distance.

ΔHvap is the energy needed to vaporize one mole of a substance from its liquid phase to the gas phase at constant pressure.

ΔHvap may also be reported as heat per gram, in which case it is the specific heat of vaporization.

ΔHvap is always positive, since vaporization is an endothermic process.

ΔHfus is the energy needed to melt one mole of a substance from its solid phase to its liquid phase at constant pressure.

ΔHfus may also be reported as heat per gram, in which case it is the specific heat of fusion.

ΔHfus is always positive, since melting is an endothermic process.

Work = Δ(PV)

At constant pressure, W = PΔV

More generally, the work done during a thermodynamic process is the area under the curve of a P vs V diagram.